Orthogonal prediction of counterfactual outcomes

Orthogonal meta-learners, such as DR-learner, R-learner and IF-learner, are increasingly used to estimate conditional average treatment effects. They improve convergence rates relative to na\"{\i}ve meta-learners (e.g., T-, S- and X-learner) through de-biasing procedures that involve applying standard learners to specifically transformed outcome data. This leads them to disregard the possibly constrained outcome space, which can be particularly problematic for dichotomous outcomes: these typically get transformed to values that are no longer constrained to the unit interval, making it difficult for standard learners to guarantee predictions within the unit interval. To address this, we construct orthogonal meta-learners for the prediction of counterfactual outcomes which respect the outcome space. As such, the obtained i-learner or imputation-learner is more generally expected to outperform existing learners, even when the outcome is unconstrained, as we confirm empirically in simulation studies and an analysis of critical care data. Our development also sheds broader light onto the construction of orthogonal learners for other estimands.